feat: screen capture scaling / downsampling

Add a Scale option (1.0 native, 0.5 half, etc.) that downsamples the
captured BGRA frame with bilinear interpolation before JPEG encoding.
Config carries the scale factor; the GUI exposes a Scale dropdown
(100%/75%/50%/25%) that applies live via SetConfig.

Verified: OBS displays the image at the reduced resolution matching the
selected scale, without restarting the stream.

internal/flinger/flinger_test.go

@@ -5,6 +5,8 @@ import (
 	"net"
 	"testing"
 	"time"
+
+	"teleportfling/internal/capture"
 )
 
 // TestEnginePatternStartStop runs the engine with the synthetic pattern source
@@ -186,6 +188,59 @@ func TestFormatBitrate(t *testing.T) {
 	}
 }
 
+// TestScaleBGRA verifies downsampling produces the expected dimensions and
+// preserves the dominant colour of a solid frame.
+func TestScaleBGRA(t *testing.T) {
+	src := &capture.VideoFrame{
+		Pix:    make([]byte, 100*80*4),
+		Width:  100,
+		Height: 80,
+		Stride: 100 * 4,
+	}
+	// Fill with solid red (BGRA: B=0, G=0, R=255).
+	for i := 0; i+4 <= len(src.Pix); i += 4 {
+		src.Pix[i], src.Pix[i+1], src.Pix[i+2], src.Pix[i+3] = 0, 0, 255, 255
+	}
+
+	dst := &capture.VideoFrame{
+		Pix:    make([]byte, 50*40*4),
+		Width:  50,
+		Height: 40,
+		Stride: 50 * 4,
+	}
+	scaleBGRA(src, dst)
+
+	if dst.Width != 50 || dst.Height != 40 {
+		t.Errorf("dst dims = %dx%d, want 50x40", dst.Width, dst.Height)
+	}
+	// Check a few pixels are solid red.
+	for _, idx := range []int{0, 4, 100, 200} {
+		if dst.Pix[idx] != 0 || dst.Pix[idx+1] != 0 || dst.Pix[idx+2] != 255 {
+			t.Errorf("pixel %d not red: B=%d G=%d R=%d", idx, dst.Pix[idx], dst.Pix[idx+1], dst.Pix[idx+2])
+		}
+	}
+}
+
+// TestEngineScalePreservesNative verifies scaleFrame returns the original
+// frame at scale 1.0.
+func TestEngineScalePreservesNative(t *testing.T) {
+	cfg := DefaultConfig()
+	cfg.Source = "pattern"
+	cfg.Port = 19760
+	eng, err := New(cfg)
+	if err != nil {
+		t.Fatalf("New: %v", err)
+	}
+
+	frame := &capture.VideoFrame{Pix: make([]byte, 4*4*4), Width: 4, Height: 4, Stride: 16}
+	if got := eng.scaleFrame(frame, 1.0); got != frame {
+		t.Error("scale 1.0 should return the original frame")
+	}
+	if got := eng.scaleFrame(frame, 0.5); got == frame {
+		t.Error("scale 0.5 should return a new frame")
+	}
+}
+
 func itoa(v int) string {
 	if v == 0 {
 		return "0"